Maths-
General
Easy
Question
Write the solutions to the given equation.
Rewrite them as the linear-quadratic system of equations and graph them to solve.
Hint:
A quadratic equation is when the polynomial has a degree two. A graph is a geometrical representation of an equation.
We are asked to solve the equation graphically by arranging them in a linear-quadratic equation.
The correct answer is: We are asked to solve the equation graphically by arranging them in a linear-quadratic equation.
Step 1 of 2:
The given equation is .
Re arranging them, we get:
Here, once we rearrange it, we multiply the equation with ten to remove the decimal. Then, take out five to factorize into the simplest form.
Step 2 of 2:
Graph the equation to get the solution:
. 
Thus, the solution of the equation is:
.
A lot of the quadratic equations can be solved using identities and factorization. You would get a maximum of two solutions for each quadratic equation.
Related Questions to study
Maths-
Prove the following statement.
The length of any one median of a triangle is less than half the perimeter of the triangle.
Answer:
c < a + b
solution:
Side AB = a
Side BC = b
Side AC = c
And median AM be Ma
AM is median so M is midpoint of BC
BM =
So, according to triangle inequality theorem,
Ma < a + ---- eq. 1
In △ACM,
AM is median so M is midpoint of BC
MC =
So, according to triangle inequality theorem,
Ma < c + ---- eq. 2
Add eq. 1 and eq. 2.
Ma + Ma < a + + c +
2Ma < a + b + c
Ma <
- Hints:
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c
c < a + b
- The line segment which joins the vertex of triangle to midpoint of opposite side is called the ‘median’.
- Perimeter of triangle is sum of sides.
- Perimeter = a + b + c
- To prove:
- The length of any one median of a triangle is less than half the perimeter of the triangle.
solution:
- Step 1:
Side AB = a
Side BC = b
Side AC = c
And median AM be Ma
- Step 2:
AM is median so M is midpoint of BC
BM =
So, according to triangle inequality theorem,
Ma < a +
---- eq. 1In △ACM,
AM is median so M is midpoint of BC
MC =
So, according to triangle inequality theorem,
Ma < c +
---- eq. 2Add eq. 1 and eq. 2.
Ma + Ma < a +
+ c + 2Ma < a + b + c
Ma <
- Final Answer:
Prove the following statement.
The length of any one median of a triangle is less than half the perimeter of the triangle.
Maths-General
Answer:
c < a + b
solution:
Side AB = a
Side BC = b
Side AC = c
And median AM be Ma
AM is median so M is midpoint of BC
BM =
So, according to triangle inequality theorem,
Ma < a + ---- eq. 1
In △ACM,
AM is median so M is midpoint of BC
MC =
So, according to triangle inequality theorem,
Ma < c + ---- eq. 2
Add eq. 1 and eq. 2.
Ma + Ma < a + + c +
2Ma < a + b + c
Ma <
- Hints:
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c
c < a + b
- The line segment which joins the vertex of triangle to midpoint of opposite side is called the ‘median’.
- Perimeter of triangle is sum of sides.
- Perimeter = a + b + c
- To prove:
- The length of any one median of a triangle is less than half the perimeter of the triangle.
solution:
- Step 1:
Side AB = a
Side BC = b
Side AC = c
And median AM be Ma
- Step 2:
AM is median so M is midpoint of BC
BM =
So, according to triangle inequality theorem,
Ma < a +
---- eq. 1In △ACM,
AM is median so M is midpoint of BC
MC =
So, according to triangle inequality theorem,
Ma < c +
---- eq. 2Add eq. 1 and eq. 2.
Ma + Ma < a +
+ c + 2Ma < a + b + c
Ma <
- Final Answer:
General
Select the three most common text features
Correct answer a) Title, 6) Table of Content d) Picture of and Captions
Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body
Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body
Select the three most common text features
GeneralGeneral
Correct answer a) Title, 6) Table of Content d) Picture of and Captions
Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body
Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body
Maths-
Solve 3.5x+19≥1.5x-7
Hint:
Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .
We are asked to solve the inequality.
Step 1 of 1:
Rearrange and solve the inequality,
Note:
Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.
Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .
We are asked to solve the inequality.
Step 1 of 1:
Rearrange and solve the inequality,
Note:
Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.
Solve 3.5x+19≥1.5x-7
Maths-General
Hint:
Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .
We are asked to solve the inequality.
Step 1 of 1:
Rearrange and solve the inequality,
Note:
Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.
Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .
We are asked to solve the inequality.
Step 1 of 1:
Rearrange and solve the inequality,
Note:
Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.
Maths-
Determine whether each graph represents a function ?
Step by step solution:
We consider the first graph.
We can observe that any vertical line drawn on the graph cuts the line at exactly one point
Hence, this graph represents a function.
The second graph is
Again, we can observe that any vertical line drawn cuts the graph at exactly one point.
Hence, this graph is also a function.
Finally, consider the third graph.
If we draw a vertical line at the origin, that is, the y-axis, we can see that it cuts the graph at two points.
Thus, this graph is not a function.
We consider the first graph.
We can observe that any vertical line drawn on the graph cuts the line at exactly one point
Hence, this graph represents a function.
The second graph is
Again, we can observe that any vertical line drawn cuts the graph at exactly one point.
Hence, this graph is also a function.
Finally, consider the third graph.
If we draw a vertical line at the origin, that is, the y-axis, we can see that it cuts the graph at two points.
Thus, this graph is not a function.
Determine whether each graph represents a function ?
Maths-General
Step by step solution:
We consider the first graph.
We can observe that any vertical line drawn on the graph cuts the line at exactly one point
Hence, this graph represents a function.
The second graph is
Again, we can observe that any vertical line drawn cuts the graph at exactly one point.
Hence, this graph is also a function.
Finally, consider the third graph.
If we draw a vertical line at the origin, that is, the y-axis, we can see that it cuts the graph at two points.
Thus, this graph is not a function.
We consider the first graph.
We can observe that any vertical line drawn on the graph cuts the line at exactly one point
Hence, this graph represents a function.
The second graph is
Again, we can observe that any vertical line drawn cuts the graph at exactly one point.
Hence, this graph is also a function.
Finally, consider the third graph.
If we draw a vertical line at the origin, that is, the y-axis, we can see that it cuts the graph at two points.
Thus, this graph is not a function.
General
Choose the negative adjectives starting with ' u '
Correct answer a) unattractive.
Explanation-Negative adjectives are the word that explains / pronounce negatively.
Explanation-Negative adjectives are the word that explains / pronounce negatively.
Choose the negative adjectives starting with ' u '
GeneralGeneral
Correct answer a) unattractive.
Explanation-Negative adjectives are the word that explains / pronounce negatively.
Explanation-Negative adjectives are the word that explains / pronounce negatively.
Maths-
Describe the possible values of x.
- Step-by-step explanation:
- Given:
a = x + 11, b = 2x + 10, and c = 5x - 9.
- Step 1:
- First check validity.
According to triangle inequality theorem,
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
x + 11 < 7x + 1,
11 – 1 < 7x - x
10 < 6x
< x,
1.6 < x
Now, consider,
3x - 19 < x + 11
3x - x < 11 + 19
2x < 30
x < 
,
x < 15
therefore,
1.6 < x < 15
- Final Answer: